Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
| Autor: | T. M. Rocha Filho, M. A. Amato, L. H. Miranda Filho |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Physics Statistical Mechanics (cond-mat.stat-mech) Thermodynamic equilibrium FOS: Physical sciences Statistical and Nonlinear Physics Statistical mechanics Lyapunov exponent 01 natural sciences Chaos theory 010305 fluids & plasmas symbols.namesake Mean field theory 0103 physical sciences Thermodynamic limit symbols Statistical physics Statistics Probability and Uncertainty 010306 general physics Hamiltonian (quantum mechanics) Critical exponent Condensed Matter - Statistical Mechanics |
| DOI: | 10.48550/arxiv.1704.02678 |
| Popis: | We investigate the dependence of the largest Lyapunov exponent of a $N$-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the largest Lyapunov exponent, although at variance with the theoretical estimate. The existence of chaos in the magnetized state evidenced by a positive Lyapunov exponent, even in the thermodynamic limit, is explained by the resonant coupling of individual particle oscillations to the diffusive motion of the center of mass of the system due to the thermal excitation of a classical Goldstone mode. The transition from "weak" to "strong" chaos occurs at the onset of the diffusive motion of the center of mass of the non-homogeneous equilibrium state, as expected. We also discuss thoroughly for the model the validity and limits of a geometrical approach for their analytical estimate. Comment: 21 pages, 14 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|